Question: The sum of $5$ consecutive integers is $500$. What is the fourth number in this sequence?
Answer: Call the first number in the sequence $x$ The next integer in the sequence is $x + 1$ The sum of the $5$ consecutive integers is: $x+ (x + 1)+ (x + 2)+ (x + 3)+ (x + 4) = 500$ $5x + 10= 500$ $5x = 490$ $x = 98$ Since $x$ is the first number, $x + 3$ is the fourth integer. Thus, the fourth number in the sequence is $101$.